Question

If $f$ is a function such that $f\left(0\right)=2,f\left(1\right)=3$ and $f(x+2)=2f\left(x\right)–f(x+1)$ for every real $x$, then $f\left(5\right)–10=$ ___

Answer 1

$\because x=0\Rightarrow f\left(2\right)=2f\left(0\right)-f\left(1\right)=2\times 2-3=1$

$x=1\Rightarrow f\left(3\right)=2f\left(1\right)-f\left(2\right)=2\times 3-1=5$

$x=2\Rightarrow f\left(4\right)=2f\left(2\right)-f\left(3\right)=2\times 1-5=-3$

$x=3\Rightarrow f\left(5\right)=2f\left(3\right)-f\left(4\right)=2\times 5-(-3)=13$